Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor's: G. I. MIRUMBE and V. A. SSEMBATYA
Pages: [75] - [92]
Received Date: September 30, 2012
Submitted by:
Given an ordinary differential equation with polynomial coefficients,
Wiener and Cooke [5] gave a necessary and sufficient condition for the
simultaneous existence of solutions to ordinary differential equations
with polynomial coefficients in the form of finite order linear
combination of the Dirac delta function and its derivatives and the
rational function solutions by using the Laplace transform and
functional differential equations techniques.
In this paper, we prove a similar result by using the theory of
boundary values and the Cauchy transform. This method has an advantage
over the method in Wiener and Cooke [5] as it gives a closed form
expression for the resulting polynomial in case the finite order
distributional solution and the rational function solution do not
satisfy similar differential equations.
Cauchy transforms, singular distributions, Dirac delta function, boundary values.
